The radius of a sphere is measured to be $$7.50$$±$$0.85cm$$. Suppose the percentage error in its volume is x. The value of x, to the nearest x, $$is_____$$

Volume of sphere, $$V=43$$$$π$$$$R3$$Δ$$VV=3$$Δrr ⇒ΔVV×$$100=3$$Δrr×$$100$$⇒ΔVV×$$100=3$$×$$0.857.50$$×$$100=34$$%

Accuracy; precision of instruments and errors in measurements

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Question

The radius of a sphere is measured to be $(7.50 \pm 0.85) c m$ . Suppose the percentage error in its volume is x. The value of x, to the nearest x, is_____

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Solution

$\begin{array}{l} Volume of sphere, V = \frac{4}{3} π R^{3} \\ \frac{Δ V}{V} = \frac{3 Δ r}{r} \\ \Rightarrow \frac{Δ V}{V} \times 100 = \frac{3 Δ r}{r} \times 100 \\ \Rightarrow \frac{Δ V}{V} \times 100 = 3 \times \frac{0.85}{7.50} \times 100 = 34 % \end{array}$

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